The negative binomial can be applied in any situation in which there is a series of independent trials, each of which can result in either of just two outcomes. The distribution applies to the number of trials that occur before the designated outcome occurs. For example, if you start flipping a fair coin repeatedly the negative binomial distribution gives the number of times you must flip the coin until you see 'heads'. There are also 'everyday' applications in inventory control and the insurance industry. Please see the link.
Use the continuity correction when using the normal distribution to approximate a binomial distribution to take into account the binomial is a discrete distribution and the normal distribution is continuous.
Binomial distribution is learned about in most statistic courses. You could use them in experiments when there are two possible outcomes and each experiment is independent.
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Unless your "everyday life" involves work in some area of engineering, you won't use matrices in your everyday life.
The negative binomial can be applied in any situation in which there is a series of independent trials, each of which can result in either of just two outcomes. The distribution applies to the number of trials that occur before the designated outcome occurs. For example, if you start flipping a fair coin repeatedly the negative binomial distribution gives the number of times you must flip the coin until you see 'heads'. There are also 'everyday' applications in inventory control and the insurance industry. Please see the link.
It is necessary to use a continuity correction when using a normal distribution to approximate a binomial distribution because the normal distribution contains real observations, while the binomial distribution contains integer observations.
Use the continuity correction when using the normal distribution to approximate a binomial distribution to take into account the binomial is a discrete distribution and the normal distribution is continuous.
Binomial distribution is learned about in most statistic courses. You could use them in experiments when there are two possible outcomes and each experiment is independent.
Yes, and the justification comes from the Central Limit Theorem.
Two independent outcomes with constant probabilities.
The central limit theorem basically states that for any distribution, the distribution of the sample means approaches a normal distribution as the sample size gets larger and larger. This allows us to use the normal distribution as an approximation to binomial, as long as the number of trials times the probability of success is greater than or equal to 5 and if you use the normal distribution as an approximation, you apply the continuity correction factor.
You can use a normal distribution to approximate a binomial distribution if conditions are met such as n*p and n*q is > or = to 5 & n >30.
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If the illness is infectious then you cannot use the binomial distribution because the incidences of illness are no longer independent events, so that the assumptions required for the binomial distribution are not satisfied. Suppose the illness is not infectious and the "normal" rate of illnesses is p. Then in a group of size n, the number of units suffering has a B(n, p) distribution. You can then determine a critical region at an appropriate level of significance and test the number of victims against that.
You don't, unless you work in engineering. The Wikipedia article on "binomial theorem" has a section on "Applications".
This depends on what information you have. If you know the success probability and the total number of observations, you can use the given formulas. Most of the time, this is the case. If you have data or experience which allow you to estimate the parameters, it may sometimes happen that you work like this. This mostly happens when n is very large and p very small which results in an approximation with the Poisson distribution.